Optical element and aerial image projection device

Abstract

To provide an optical element that forms an aerial image that can be observed at a depression angle over a wide range around a horizontal axis by using a reflector array including two-surface corner reflectors.SOLUTION: An optical element 12 comprises a substrate 16 and a reflector array 17 including two-surface corner reflectors 18 distributed according to the size of reflective surfaces that are orthogonal to each other along an intersection line intersecting a surface of the substrate 16.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to an optical element comprising a plurality of dihedral corner reflectors each having two reflective surfaces that are orthogonal to each other at an intersection line that intersects the surface of a substrate. [Background technology]

[0002] As disclosed in Patent Document 1, a reflector array including dihedral corner reflectors that form retrotransmitted light using reflective surfaces that intersect at an intersection line is commonly known. In this reflector array, dihedral corner reflectors of the same shape are arranged in a matrix. The heights of all dihedral corner reflectors from the substrate are standardized to a predetermined height. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] International Publication No. 2013 / 129043 [Patent Document 2] Japanese Patent Application Laid-Open No. 2012-163701 [Non-patent literature]

[0004] [Non-Patent Document 1] Yuta Yoshimizu, Eiji Iwase, “Radially Arranged Dihedral Corner Reflector Array for Wide Viewing Angle of Floating Image without Virtual Image”, Optics Express, January 21, 2019, vol.27, issue 2, pp918-927 Summary of the Invention [Problem to be solved by the invention]

[0005] Aerial images are formed at a specific position relative to the substrate. Because the viewing angle of an aerial image is narrow, if the observer's eye position shifts, the aerial image will quickly disappear from the observer's field of vision. As disclosed in Patent Document 2 and Non-Patent Document 1, attempts have been made to ensure a wide viewing angle for aerial images around a vertical axis perpendicular to the substrate. On the other hand, no dihedral corner reflector reflector array has yet been proposed that forms aerial images that can be viewed over a wide range of depression angles around a horizontal axis parallel to the substrate.

[0006] The present invention aims to provide an optical element that uses a reflector array including dihedral corner reflectors to form an aerial image that can be observed over a wide range of depression angles around a horizontal axis. [Means for solving the problem]

[0007] An optical element according to one aspect of the present invention includes a substrate and a reflector array including dihedral corner reflectors distributed according to the size of reflecting surfaces that intersect at a line of intersection on the surface of the substrate.

[0008] An aerial image projection device according to one embodiment of the present invention comprises a substrate, a reflector array including dihedral corner reflectors distributed according to the size of the reflective surfaces that intersect at a line of intersection that intersects the surface of the substrate, and a light source that faces the back surface of the substrate at a position corresponding to the dihedral corner reflector that emits retrotransmitted light with the maximum depression angle. [Effects of the Invention]

[0009] As described above, according to the disclosed embodiments, an optical element can be provided that uses a reflector array including a dihedral corner reflector to form an aerial image that can be observed at a wide range of depression angles around a horizontal axis. [Brief explanation of the drawings]

[0010] [Figure 1] 1 is a schematic diagram illustrating the configuration of an aerial image projection device according to a first embodiment of the present invention. [Figure 2] FIG. 1 is a conceptual diagram of an optical element. [Figure 3] This is a partial cross-sectional view taken along line 3-3 in Figure 2, and is a conceptual diagram showing the effect of the height of the dihedral corner reflector on the aerial image. [Figure 4] FIG. 10 is a conceptual diagram of an optical element according to another specific example. [Figure 5] This is a conceptual diagram (photo) showing the radial arrangement of dihedral corner reflectors. [Figure 6] FIG. 1 is a conceptual diagram showing the relationship between the size of the reflecting surface of a dihedral corner reflector and the amount of retrotransmitted light. [Figure 7] 1 is a graph showing the relationship between the angle of incidence and retrotransmitted light. [Figure 8] 10 is a graph showing the relationship between the distance from the center of the distribution and retrotransmitted light. [Figure 9] 1 is a graph showing the height distribution of a dihedral corner reflector versus the angle of incidence. [Figure 10] 1 is a graph showing the relationship between the angle of incidence and retrotransmitted light. [Figure 11] 10 is a graph showing the relationship between the distance from the center of the distribution and retrotransmitted light. [Figure 12] 1 is a graph showing the height distribution of a dihedral corner reflector versus the angle of incidence. [Figure 13] 1 is a graph showing the relationship between the angle of incidence and retrotransmitted light. [Figure 14] 10 is a graph showing the relationship between the distance from the center of the distribution and retrotransmitted light. [Figure 15] FIG. 4 is a schematic diagram illustrating the configuration of an optical element according to a second embodiment of the present invention. [Figure 16] This is a conceptual diagram showing the effect of the side length of a dihedral corner reflector on the aerial image. DETAILED DESCRIPTION OF THE INVENTION

[0011] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings.

[0012] FIG. 1 shows a schematic configuration of an aerial image projection device 11 according to a first embodiment of the present invention. The aerial image projection device 11 includes a flat optical element 12 and a light source 13 facing the optical element 12 at a predetermined position. A display panel, for example, is used as the light source 13. A video signal (image signal) is supplied to the display panel from, for example, a display circuit. An image is displayed on the screen 13a of the display panel in accordance with the supplied video signal. The image can include both moving images and still images. The image is projected toward the rear surface of the optical element 12. The optical element 12 can focus the image of the light source 13 at a position perpendicular to its front surface. An aerial image can be formed based on the image of the light source 13. The screen 13a of the display panel faces the rear surface of the optical element 12 at a position corresponding to a specified range 14.

[0013] As shown in Fig. 2, the optical element 12 includes a substrate 16 and a reflector array 17 disposed on the surface of the substrate 16. The substrate 16 is light-transmitting. The substrate 16 is made of, for example, glass. A screen 13a of a display panel faces the rear surface of the substrate 16. When the screen 13a of the display panel is projected perpendicularly onto the rear surface of the substrate 16, the projected image of the screen 13a falls within a specified range 14.

[0014] The reflector array 17 includes a plurality of dihedral corner reflectors 18 that stand perpendicularly from the surface of the substrate 16. The dihedral corner reflectors 18 are molded from a transparent material. Each dihedral corner reflector 18 is formed as a rectangular prism whose square bottom surface 18a is bonded to the surface of the substrate 16. The rectangular prism has a uniform cross-sectional shape from the bottom surface 18a to the top surface 18b. The side surfaces of the rectangular prism form reflective surfaces 19 depending on the material and the refractive index of the atmosphere. The reflective surfaces 19 intersect at right angles at an intersection line 21. The intersection line 21 intersects the surface of the substrate 16 perpendicularly. The top surface 18b of the rectangular prism is perpendicular to the intersection line 21 and extends parallel to the bottom surface 18a. The surface of the substrate 16 is formed as a single plane. Note that in a dihedral corner reflector 18, at least two reflective surfaces 19 must be perpendicular to the intersection line 21, and the side surfaces facing these reflective surfaces 19 may intersect the surface of the substrate 16 at an inclination angle of less than 90°. Alternatively, the dihedral corner reflector 18 may have the reflecting surface 19 formed by openings or slits drilled in the substrate 16, or may have the reflecting surface 19 formed by a three-dimensional structure assembled from sheet materials.

[0015] In the reflector array 17, the dihedral corner reflectors 18 are distributed according to the size of the reflecting surface 19. Here, the size of the reflecting surface 19 is set by the height of the rectangular prism (length of the intersection line). The side length of the bottom surface 18a is standardized to a single value. The spacing between the dihedral corner reflectors 18 is also standardized to a single value. The dihedral corner reflectors 18 are distributed according to a predetermined height. When distributed, the dihedral corner reflectors 18 form clusters in each region. The height of the rectangular prism is made uniform in each region.

[0016] Figure 2 conceptually depicts the height distribution. The curved surface shapes shown in the wireframe correspond to the top surfaces 18b of the individual rectangular prisms. In the central cluster, the heights of the dihedral corner reflectors 18 are aligned to the maximum height. The cluster of dihedral corner reflectors 18 with the maximum height is placed within a specified range 14. The heights are aligned according to the distance away from the dihedral corner reflector 18 with the maximum height. The height decreases as the distance increases. As shown in Figure 3, the height decreases in stages.

[0017] Next, the operation of the aerial image projection device 11 will be described. As shown in FIG. 3, the image of the light source 13 is reflected by each dihedral corner reflector 18 and projected above the substrate 16. Aerial images are formed. Light incident on the bottom surface 18a of each dihedral corner reflector 18 exits from the top surface 18b as retrotransmitted light. The size of the two reflective surfaces 19 determines the angle of incidence of the retrotransmitted light. By distributing the dihedral corner reflectors 18 according to the size of their reflective surfaces 19, exit light with various depression angles θ can be formed. In this way, aerial images 22a, 22b, and 22c can be formed that can be viewed at a wide range of depression angles around the horizontal axis: θlarge, θmedium, and θsmall.

[0018] In the reflector array 17 according to this embodiment, the dihedral corner reflectors 18 are distributed at predetermined heights h. The size of the reflective surface 19 varies depending on the height h of the dihedral corner reflectors 18. The angle of incidence of retrotransmitted light can be determined by designing the height h of the dihedral corner reflectors 18. By distributing the dihedral corner reflectors 18 at predetermined heights h, exit light with various depression angles can be generated. In this way, an aerial image can be formed that can be observed at a wide range of depression angles around the horizontal axis. Within the reflector array 17, the side length p of the bottom surface 18a is unified to a single value despite size variations. The spacing between the dihedral corner reflectors 18 can be set to a minimum value. The total amount of retrotransmitted light can be maximized relative to the amount of incident light throughout the reflector array 17.

[0019] In the reflector array 17, the height h of the dihedral corner reflectors 18 is made uniform depending on the distance from the dihedral corner reflector 18 with the greatest height. A group (assembly) of dihedral corner reflectors 18 can be formed for each height h. The depression angle of the emitted light can be set for each formed group. Good resolution can be ensured for each depression angle. If the height of the dihedral corner reflectors 18 changes in stages, the complexity of the manufacturing process for the dihedral corner reflectors 18 can be reduced compared to when the height decreases gradually. For example, if photolithography is used to form the reflector array 17, processes such as exposure and development must be repeated for each distributed height.

[0020] In this embodiment, the height h of the dihedral corner reflectors 18 decreases as the distance from the dihedral corner reflector 18 with the greatest height increases. The height h of the dihedral corner reflectors 18 decreases as the distance from the dihedral corner reflector 18 with the greatest height increases. Even if the heights h vary, interference between the dihedral corner reflectors 18 and the emitted light can be effectively avoided. As shown in FIG. 4 , the height h may decrease radially from the collection with the greatest height at the center. In this case, a collection of dihedral corner reflectors 18 can be formed in a ring shape at each height h. FIG. 5 illustrates the concept of a radial arrangement. This radial arrangement allows for the formation of an aerial image with a wide viewing angle around a vertical axis perpendicular to the substrate 16. Note that although FIG. 5 illustrates the concept of a radial arrangement, the heights of the dihedral corner reflectors are unified to a single value. Alternatively, the height h may decrease from the collection with the greatest height arranged along one side of the substrate 16 toward the opposite side. In this case, a group of dihedral corner reflectors 18 can be formed linearly at every height h.

[0021] As shown in Figure 6, a specific relationship exists between the amount of retrotransmitted light and the size of the reflecting surface 19 in the dihedral corner reflector 18. To clarify this relationship, the rectangular prism of the dihedral corner reflector 18 stands upright with a uniform cross section from the square base 18a. The height h of the rectangular prism corresponds to the height of the reflecting surface 19. The side length p of the base 18a corresponds to the width of the reflecting surface 19. Light is represented by the incident angle θ projected onto the side of the rectangular prism. In Figure 6A, light 24 enters the dihedral corner reflector 18 from the bottom surface 18a at an incident angle θi. Within the dihedral corner reflector 18, light 24 is reflected twice by the two reflecting surfaces 19 and exits from the top surface 18b. All incident light at an incident angle θi can be used as retrotransmitted light. A ratio R of retrotransmitted light to incident light of 1 is achieved. In Figure 6B, the incident angle θ is smaller than the incident angle θi. In this case, although light 25 is partially retrotransmitted within the dihedral corner reflector 18, it passes through the top surface 18b without reaching the second reflecting surface 19. Therefore, the ratio R of the retrotransmitted light to the incident light can be determined by the following equation:

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[0022] Next, the inventors examined the design requirements for the reflector array 17 based on the derived relationship. In their examination, the inventors set the incident angle θ to be greater than 20° and less than 70°. They assumed that dihedral corner reflectors were formed in a matrix of 350 x 350 on a 40 mm x 50 mm glass substrate. The side length of the bottom surface of the dihedral corner reflector was set to 60 μm. The spacing between dihedral corner reflectors was set to 30 μm. As shown in Figure 7, when the height of the dihedral corner reflectors was set to a single value, it was confirmed that all incident light was emitted as retrotransmitted light at a specific incident angle θs. When the height of the dihedral corner reflector was set according to [Equation 4], it was confirmed that all incident light was emitted as retrotransmitted light at incident angles θ ranging from 20° to 70°. Assuming that a good aerial image can be observed when the proportion of retrotransmitted light is 0.8 (80%) or higher, it was confirmed that a viewing angle of 56.94° was secured at a height set according to [Equation 4], while a viewing angle of 11.51° was obtained at a uniform height. As shown in Figure 8, retrotransmitted light was confirmed over a wide range, centered on the dihedral corner reflector at the maximum height.

[0023] Generally, photolithography and other techniques are used for microfabrication of the reflector array 17. Up until now, in such microfabrication, a processing process is performed for each height of the dihedral corner reflector, so setting the height of the dihedral corner reflector in a continuous manner is not realistic in terms of time, cost, and various other aspects. As shown in Figure 9, the inventors have considered the constraints of such height distribution and have examined a reflector array 17 with a height distribution realized in three stages. First, the incident angle θi that maximizes the retrotransmitted light for each i-th stage is calculated based on the following equation. At this time, the incident angle θ exceeds θ1 [°] and becomes θ n It is set to a range of less than [°].

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[0024] The inventors further investigated a reflector array 17 with a height distribution in which the height change is constrained to an integer multiple of the minimum height, as shown in FIG. 12 . Under similar conditions, when the incident angle θ was set to greater than 20° and less than 70°, a retrotransmitted light ratio of 0.8 or greater was ensured across the incident angle θ range of 20° to 70°, as shown in FIG. 13 . This is expected to enable the observation of good aerial images. Despite the constraint of a height distribution that is achieved by an integer multiple of the minimum height, a viewing angle of 29.59° was confirmed. As shown in FIG. 14 , assuming the distance d between the light source 13 and the reflector array 17 is set to 0.2 m and the total length of the reflector array 17 is set to 1.131 m, the boundary between the dihedral corner reflector 18 with the maximum height and the dihedral corner reflector 18 with the next highest height was calculated to be 0.227 m from the center of the distribution. The proportion of dihedral corner reflectors 18 with the maximum height was 20.1% of the total. The boundary line between the dihedral corner reflectors 18 of the next highest height and the dihedral corner reflectors 18 of the minimum height was calculated to be 0.378 m from the center. The proportion of dihedral corner reflectors 18 of the next highest height was 33.4% of the total. The proportion of dihedral corner reflectors 18 of the minimum height was 46.5% of the total.

[0025] FIG. 15 schematically illustrates the structure of an optical element 31 according to a second embodiment of the present invention. The optical element 31 includes the aforementioned substrate 16 and a reflector array 32 disposed on the surface of the substrate 16. The reflector array 32 includes a plurality of dihedral corner reflectors 33 extending perpendicularly from the surface of the substrate 16. The dihedral corner reflectors 33 are molded from a transparent material. As shown in FIG. 16, the dihedral corner reflectors 33 are formed as square prisms with a square bottom surface 33a bonded to the surface of the substrate 16. The square prism has a uniform cross-sectional shape from the bottom surface 33a to the top surface 33b. The side surfaces of the square prism form reflective surfaces 34 depending on the refractive index of the material and the atmosphere. The reflective surfaces 34 intersect at right angles at an intersection line 35. The intersection line 35 perpendicularly intersects the surface of the substrate 16. The top surface 33b of the square prism is perpendicular to the intersection line 35 and extends parallel to the bottom surface 33a. The surface of the substrate 16 is formed as a single plane. In the dihedral corner reflector 33, it is sufficient that at least two reflective surfaces 34 are perpendicular to each other at an intersection line 35, and the side surfaces facing these reflective surfaces 34 may intersect with the surface of the substrate 16 at an inclination angle of less than 90°. Alternatively, the dihedral corner reflector 33 may form the reflective surfaces 34 based on openings or slits made in the substrate 16, or based on a three-dimensional structure assembled from sheet materials.

[0026] In the reflector array 32, the dihedral corner reflectors 33 are distributed according to the size of the reflecting surface 34. Here, the size of the reflecting surface 34 is set by the side length of the base surface 33a. The height of the rectangular prism is standardized to a single value. The spacing between the dihedral corner reflectors 33 is adjusted based on the side length. The dihedral corner reflectors 33 are distributed according to a predetermined side length. When distributed, the dihedral corner reflectors 33 form clusters in each region. The side length of the base surface 33a in each region is made uniform.

[0027] Similar to the height distribution, the side lengths of the dihedral corner reflectors 33 in the central cluster are aligned to a minimum value. Clusters of dihedral corner reflectors 33 with the minimum side length are arranged within a specified range 14. The side lengths are aligned according to the distance away from the dihedral corner reflector 33 with the minimum side length. The side lengths increase as the distance increases.

[0028] As shown in Figure 16, the image of the light source 13 is reflected by each dihedral corner reflector 33 and projected above the substrate 16. An aerial image is formed. In each dihedral corner reflector 33, light incident on the bottom surface 33a exits from the top surface 33b as retrotransmitted light. The size of the two reflective surfaces 34 determines the angle of incidence of the retrotransmitted light. By distributing the dihedral corner reflectors 33 according to the size of the reflective surface 34, output light with various depression angles θ can be formed. In this way, aerial images 36a, 36b, and 36c can be formed that can be observed at a wide range of depression angles around the horizontal axis: θlarge, θmedium, and θsmall.

[0029] In the reflector array 32 of this embodiment, the dihedral corner reflectors 33 are distributed every predetermined side length p. The size of the reflective surface 34 varies depending on the side length p of the dihedral corner reflector 33. The angle of incidence of retrotransmitted light can be determined by designing the side length p of the dihedral corner reflector 33. By distributing the dihedral corner reflectors 33 every predetermined side length p, exit light with various depression angles can be formed. In this way, aerial images can be formed that can be observed at a wide range of depression angles around the horizontal axis. Within the reflector array 32, the height h of the dihedral corner reflectors 33 is unified to a single value despite size variations. Using photolithography technology, the dihedral corner reflectors 33 can be formed with a single exposure. This simplifies the manufacturing process, and improved yields can be expected.

[0030] In the reflector array 32, the side length p of the dihedral corner reflectors 33 is made uniform depending on the distance away from the dihedral corner reflector 33 with the smallest side length. A group (assembly) of dihedral corner reflectors 33 can be formed for each side length p. The depression angle of the emitted light can be set for each formed group. Good resolution can be ensured for each depression angle.

[0031] In this embodiment, the side length p of the dihedral corner reflectors 33 increases with increasing distance from the dihedral corner reflector 33 with the minimum side length. The side length p of the dihedral corner reflectors 33 also increases with increasing distance from the dihedral corner reflector 33 with the minimum side length. Similar to the height distributions shown in FIGS. 2 and 4 , the side length p may increase radially from the cluster of dihedral corner reflectors 33 with the minimum side length at the center. In this case, a ring-shaped cluster of dihedral corner reflectors 33 can be formed for each side length p. This radial arrangement allows for the formation of an aerial image with a wide viewing angle around a vertical axis perpendicular to the substrate 16. Alternatively, the side length p may increase from the cluster of dihedral corner reflectors 33 with the minimum side length arranged along one side of the substrate 16 toward the opposite side. In this case, a linear cluster of dihedral corner reflectors 33 can be formed for each side length p. [Explanation of symbols]

[0032] 11 Aerial image projection device 12 Optical Elements 13 Light source 17 Reflector Array 18 Two-sided corner reflector 19 Reflective surface 21 Intersection line 31 Optical Elements 32 Reflector Array 33 2-sided corner reflector 34 Reflective surface 35 Intersection line h height p side length

Claims

1. A substrate; a reflector array including dihedral corner reflectors distributed according to the size of the reflecting surfaces that intersect at a line of intersection that intersects with the surface of the substrate; An optical element comprising:

2. The dihedral corner reflectors are distributed at intervals of the determined length of the intersection line. The optical element according to claim 1 .

3. The length is adjusted according to the distance from the dihedral corner reflector having the maximum length. The optical element according to claim 2 .

4. As the distance increases, the length decreases. The optical element according to claim 3 .

5. As the distance increases, the length decreases in stages. The optical element according to claim 4 .

6. The dihedral corner reflectors are distributed according to the side lengths obtained in a cross section perpendicular to the intersection line. The optical element according to claim 1 .

7. The side lengths are adjusted according to the distance from the dihedral corner reflector with the smallest side length. The optical element according to claim 6 .

8. As the distance increases, the side length increases. The optical element according to claim 7 .

9. A substrate; a reflector array including dihedral corner reflectors distributed according to the size of the reflecting surfaces that intersect at a line of intersection that intersects with the surface of the substrate; a light source facing the rear surface of the substrate at a position corresponding to the dihedral corner reflector that emits retrotransmitted light at the maximum depression angle; An aerial image projection device comprising:

Images